The sum of the squares of three consecutive odd integers is 683. what are the integers?

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Answer 1 · 2018-02-22T21:23:29

The required odd integers are #\ \ \ # #13#, #\ \ \ ##15##\ \ \ # and #\ \ \ # #17#

Let the three odd numbers be #x − 2# , #x# and #x + 2# . As sum of their squares is #683# , we have:

#(x-2)^2+x^2+(x+2)^2=683#

#x^2-4x+4+x^2+x^2+4x+4=683#

Simplify:

#3x^2+8=683#

Solve for #x# to get:

#x=15#

So, our required odd integers are#\ \ \ # #13#, #\ \ \ ##15##\ \ \ # and #\ \ \ # #17#

That's it!